Computational methods for performance analysis of horizontal axis tidal stream turbines

Applied Energy 98 (2012) 512–523

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Computational methods for performance analysis of horizontal axis tidal stream turbines Ju Hyun Lee a,1, Sunho Park a, Dong Hwan Kim a, Shin Hyung Rhee b,⇑, Moon-Chan Kim c a

Dept. of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Republic of Korea Dept. of Naval Architecture and Ocean Engineering, Research Institute of Marine Systems Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744, Republic of Korea c Dept. of Naval Architecture and Ocean Engineering, Pusan National University, Busan, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 2 January 2012 Received in revised form 2 April 2012 Accepted 12 April 2012 Available online 14 May 2012 Keywords: Tidal stream energy Horizontal axis tidal stream turbine (HATST) Blade element momentum theory (BEMT) Computational fluid dynamics (CFD)

a b s t r a c t In the present study, two computational procedures, based on the blade element momentum theory and computational fluid dynamics, were developed for open water performance prediction of horizontal axis tidal stream turbines. The developed procedures were verified by comparison with other computational results and existing experimental data and then, applied to a turbine design process. The results of the open water performance prediction were discussed in terms of the efficiency and accuracy of the design process. For better cavitation inception performance, a raked tip turbine design was proposed and analyzed with the developed procedure. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Recently, due to high oil prices and environmental pollution issues, interest in the development of alternative energy and related research has tremendously increased. Renewable energy, one form of alternative energy, utilizes energy that can be re-used, as its mechanical power source. Among the many types of renewable energy, tidal stream energy, which is caused by the ebb and flood of a tide due to the gravitational pull of the moon, has many attractive features and is known as one of the most promising energy resources. It is reliable and predictable and has the potential to minimize both visual and noise pollution [1]. Energy conversion turbine systems, utilizing tidal stream energy, can be categorized into horizontal and vertical axes, according to its rotor axis configuration. A vertical axis tidal stream turbine (VATST) has its rotational axis perpendicular to the incoming flow. Power generators are usually located above the water surface, making waterproof sealing around them unnecessary. In addition, vertical axis turbines generate less noise thanks to reduced blade tip losses. On the other hand, the rotational axis of a horizontal axis tidal stream turbine (HATST) is parallel to the incoming flow. The merits of such rotors are numerous. The literature in neighboring fields, such as wind engineering and marine propellers, is abundant. Pitch control methods to protect the rotor ⇑ Corresponding author. Tel.: +82 2 880 1500; fax: +82 2 888 9298. 1

E-mail address: [email protected] (S.H. Rhee). Present address: Samsung Heavy Industries.

0306-2619/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2012.04.018

in overly high speed have been already studied for wind engineering. Their optimum performance is generally achieved at higher revolution speeds, which eases the problem of generator matching, in other words, allows for reduced gear coupling [2]. Considering these merits, a HATST type system was selected for the present study. There are mainly two approaches for numerically analyzing the performance of a HATST system. One is the blade element momentum theory (BEMT) and the other is computational fluid dynamics (CFD). BEMT models the rotor as a set of isolated two-dimensional (2D) blade elements, to which one can apply the 2D hydrodynamics theory individually and then perform an integration to find the thrust and torque. BEMT was mainly used for the analysis of HATSTs [3–5]. In those studies, the results from model-scale experiments and BEMT were compared and discussed. On the other hand, thanks to the rapid growth of numerical methods and computer resources, CFD applications have been recently abundant. Studies using CFD were done for the analysis of three-dimensional (3D) turbines [6,7] and for the wake effect of turbines [1,8,9]. Besides the general primitive variable-based formulation, McCombes et al. [10] presented a numerical model based on the vorticity conserving form for unsteady wake modeling for marine current turbines. The present study focused on the development of efficient and convenient procedures to predict the performance of tidal stream turbines for better designs. The objectives were therefore (1) to develop and validate a BEMT code, (2) to develop a full-scale 3D CFD procedure, and (3) to suggest a new HATST design for cavitation inception delay.

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Nomenclature A a a0 B C CD CL CP Cpress CT Cx Cy D f L P p PL

swept area (m2) axial flow induction factor (-) tangential flow induction factor (-) number of blade (-) blade chord length (m) drag coefficient (-) lift coefficient (-) power coefficient (-) pressure coefficient (-) thrust coefficient (-) axial force coefficient (-) tangential force coefficient (-) rotor drag force (N) tip loss factor (-) rotor lift force (N) rotor power (W) estimated order of accuracy of the computational method (-) local pressure (Pa)

PO Q RE r R T TSR U W /

u q r rr X

The paper is organized as follows. The description of the physical problem is presented first, and this is followed by the computational methods of BEMT and CFD. The computational results are then presented and discussed. Finally, the summary and concluding remarks are made. 2. Problem description A baseline turbine design was defined to show the feasibility of the developed procedures. A three-bladed HATST with a radius of 4 m was selected. The turbine blade consisted of the NACA 63418 foil section, which is a popular blade section geometry for wind turbines. The foil shape was used from beyond the hub to the blade tip, i.e., between r/R = 0.2–1.0. Unlike wind turbines, where a circular-shaped hub fitting is generally used, a 2:1 elliptical shape was adopted for the hub fitting. Generally, an elliptical hub is stronger than a circular one in flows with less frequent changes of direction such as one in a tidal stream. The spanwise sections were designed to have various twist angles to extract a uniform lift force from each section. The chord lengths of each section ranged from 0.68 m at the root to 0.27 m at the blade tip. The axis of the twist and the center of each section were at 0.25C and 0.3C away from the leading edge, respectively. For the hub fitting part, there was no twist angle and the center was located at 0.5C. The design revolution speed, X, was 24.72 rpm. The operating speed expressed by the tip speed ratio (TSR) was defined as

TSR ¼

RX U

reference pressure (Pa) rotor torque (N) Richardson extrapolated value (-) radius of local blade element (m) radius of turbine (m) rotor thrust (N) tip speed ratio (-) free stream velocity (m/s) relative velocity at the blade (m/s) local inflow angle (°) computational solution variable for uncertainty assessment (-) density (kg/m3) cavitation number (-) solidity, CB/2p (-) rotational speed (rad/s)

operates. The first method is the momentum theory, which is used for the momentum balance on a rotating annular streamtube passing through a turbine. In momentum theory, it is assumed that the pressure loss in the rotor is due to the work done by the flow passing through the rotor. The induced velocity caused by the momentum lost in the flow in the axial and tangential directions can be calculated using the momentum theory. The second method is the blade element theory, which is used to predict the forces on a blade by the lift and drag forces generated at various spanwise blade sections. In the blade element theory, the blade is divided into a number of sections, which act independently and operate aerodynamically as 2D airfoils whose aerodynamic forces can be calculated based on the local flow conditions. Then, the forces of each section along the span are summed to calculate the forces and moments exerted on the turbine. The coupling of these two methods to set up an iterative process to examine the induced velocity and aerodynamic forces is termed BEMT. Based on the momentum theory, the thrust and torque acquired from the flow are defined as

dT ¼ 4pqr½U 2 af ð1  af Þ þ ða0 Xrf Þ2 dr

ð2Þ

dQ ¼ 4pqr 3 U Xa0 f ð1  af Þdr

ð3Þ

0

where a and a are the axial and tangential flow induction factors, respectively; f is the tip loss factor, which is calculated as

ð1Þ

where U is the free stream flow. TSR was set between 2 and 10, and the design TSR was 5.177. In the present study, TSR was varied by changing the turbine revolution speed, while keeping the inflow speed fixed, as in Bahaj et al. [11].

Table 1 Dependency test of chordwise cell counts and turbulence models. Chordwise cell counts 76

Total cell counts 24,390

Turbulence model

Wall y+

CL (10)

CD (100)

Realizable k–

105

3.54

1.01

55

3.56

1.03

57 13 1.3 1.3 1.0 1.0

3.47 3.50 3.55 3.67 3.34 3.34

1.06 1.12 1.05 0.94 1.00 0.97

e

3. Computational methods 3.1. Blade element momentum theory BEMT is one of the oldest and most commonly used computational methods for the performance analysis of wind turbines. BEMT actually combines two methods to examine how a turbine

152

37,980

Realizable k–

e 152 182 182 182 202 546

37,980 43,380 43,380 43,380 30,120 140,940

k–x SST k–x SST k–x SST RSM k–x SST k–x SST

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dQ ¼ ðdL cos / þ dD sin /Þr

Table 2 Principal particulars of the turbines for BEMT code verification.

Number of blades Rotor radius (m) Hub radius (m) Number of sections Type of airfoil Set angle (°)

2

¼

Case 1

Case 2

Case 3

Case 4

3 5.03 1.01 16 S809 6.5, 7.5

2 13.76 1.18 17 AWT27 5, 6, 7

3 35.00 1.75 19 S818, S825 4, 8

3 3.35 0.67 8 Sg6050y 0

0

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13  2 2 B R  r TSR  r=R A5 1 4 1þ f ¼ cos exp @ 2 r 1a p

ð4Þ

where B is the number of blades. On the other hand, based on the blade element theory, the thrust and torque are defined as

1 dT ¼ dL cos / þ dD sin / ¼ qCBW 2 ðC L cos / þ C D sin /Þdr 2

1 qCrBW 2 ðC L sin /  C D cos /Þdr 2

ð6Þ

where / is the local inflow angle, C is the blade chord length, and W is the relative velocity at the blade. CL and CD indicate the lift and drag coefficients, respectively. From the equilibrium state of the thrust and torque in the momentum and blade element theories, the axial and tangential flow induction factors are derived as

" # rr C 2y ð1  aÞ2 1  a af rr ¼ Cx  2 2 1  a 4 sin2 / 4 sin / ð1  af Þ 1  af

ð7Þ

a0 f rr C y 1a ¼ 1 þ a0 4 sin / cos / 1  af

ð8Þ

where rr (=CB/2pr) is the solidity and Cy is the tangential force coefficient. Then, the solution for the power gradient can be obtained as

ð5Þ

(a) Case 1

(b) Case 2

(c) Case 3

(d) Case 4

Fig. 1. Power coefficient predicted by present and WT_Perf BEMT codes.

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515

Fig. 2. Boundary conditions and domain extents.

Fig. 3. Sub-domain near the blade.

dC P 2rr x2 ð1  aÞ2 C y  TSR ¼ 2 dr R sin /

ð9Þ

In BEMT, the forces exerted on each blade section are computed by 2D foil characteristics. Therefore, data for the 2D foil characteristics are needed for the turbine analysis. Model tests can be used to examine the 2D foil characteristics, but it requires excessive costs and time to do the model tests using a wide range of angles of attack. Meanwhile, for the analysis of the flow around a hydrofoil, CFD can be a good alternative to model tests. It can capture the flow around a foil not only in the attached flow region, but also beyond the stall region. Therefore, in the present study, CFD was used

to analyze the hydrofoil characteristics. Employing this method, the performance of a newly designed turbine could be analyzed through a combination of both CFD analysis for the 2D foil characteristics and BEMT for the turbine performance analysis. To apply this method to the baseline turbine in the present study, 2D CFD analysis for the NACA 63-418 foil section, used in the baseline turbine, was carried out. To assess the uncertainty in the foil analysis, dependency tests on the chordwise cell counts and turbulence models were done. The results of the dependency test are shown in Table 1. From the dependency tests, a mesh with 202 cells in the chordwise direction and wall y+ values less than 1.0 were chosen. For turbulent closure, the k-x SST model was selected. For verification of the developed BEMT code, a comparison was made with WT_Perf, a conventional BEMT code for wind turbines. WT_Perf was developed at the National Wind Technology Center (NWTC) for the prediction of a turbine’s performance characteristics. It is a descendant of the well-known PROP code, which was developed for the analysis of propellers based on BEMT. NWTC also provides information on several turbines for the development and validation of turbine analysis codes with information that includes the principal dimensions, rotor blade geometry, aerodynamic characteristics of the blades, and operating conditions. Among them, four cases were chosen for the present verification. The principal dimensions, airfoil types, and operating conditions are shown in Table 2. The cone, yaw, and tilt angles were assumed to be zero in all cases. The comparison of the obtained results using the two codes, i.e., the present BEMT code and WT_Perf, are shown in Fig. 1. In all the

(a) Fully structured mesh

(b) Hybrid mesh Fig. 4. Pressure coefficient contours at the suction side for fully structured and hybrid meshes.

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cases, quite a close agreement was observed between the two, confirming that BEMT was correctly implemented in the present BEMT code. 3.2. Computational fluid dynamics BEMT has the ramification that one must assume a uniform inflow over the annular elements in addition to the fact that there must be zero flow normal to the streamtube boundaries [10]. Errors occur due to those assumptions and they degrade the accuracy of the BEMT analysis. Therefore, 3D full-scale CFD analysis should be better for more precise power performance prediction and detailed flow analysis of a turbine.

(a) Hybrid mesh, r/R=0.8

(c) Hybrid mesh, r/R=0.9

Fig. 2 shows the boundary conditions and domain extents designed for the present CFD procedure. The Dirichlet boundary condition, i.e., the specified value of the velocity, was applied on the inlet boundary. On the exit boundary, the reference pressure with an extrapolated velocity was applied. The symmetric condition was applied on the top and bottom boundaries. A no-slip condition was applied on the turbine blade surfaces, i.e., the relative velocity of blades were set to zero. Between the sub-domain near the turbine blade and outer sub-domains, non-matching interfaces were defined and simple linear interpolation was used for the transition of the solution through the interface. On the side boundary, to take the rotational flow into account, the flow across the two opposite planes was assumed to be identical, i.e., periodic.

(b) Structured mesh, r/R=0.8

(d) Structured mesh, r/R=0.9

Fig. 5. Pressure coefficient contours and streamlines of the cross-sections.

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The Cartesian coordinate system adopted was such that the positive x-axis was in the streamwise direction, the positive y-axis toward the right-hand side direction, and the positive z-axis in the vertically upwind direction. The origin of the coordinate system was located at the hub center. Thus, the x-axis is the rotational axis with a rotor revolving in the counter clockwise direction. In the present study, a rotating reference frame was used to accommodate the rotor revolution in the open water condition. With the rotating reference frame, only one blade needed to be modeled with periodic boundaries on the sides. The computational domain’s extent was a length of 9D and a radius of 3D, where D represents the turbine diameter. The inlet and outlet boundaries were located at 3D upstream and 6D downstream, respectively. A cell-centered finite volume method with a pressure-based velocity–pressure coupling algorithm was employed along with a linear reconstruction scheme that allows the use of computational cells with arbitrary shapes. The solution gradients at the cell centers were evaluated by the cell center-based Green Gauss method. The convection terms were discretized using a second order accurate upwind interpolation scheme, and for the diffusion terms, a central differencing scheme was used. The equations for continuity and momentum were solved sequentially [12]. The discretized algebraic equations were solved using a pointwise Gauss–Seidel iterative algorithm, while an algebraic multi-grid method was employed to accelerate solution convergence. The commercial CFD code, FLUENT v6.3, was used for carrying out the computations. To develop a convenient procedure for performance prediction, hybrid meshing was used. The whole domain was divided into several sub-domains, and among the sub-domains, the one with the blade was filled with tetrahedral cells and the others with simple geometry were filled with hexahedral cells for a high quality solution, shown in Fig. 3. By this approach, it was possible to get rid of the difficulty of mesh generation around complex geometries. Moreover, design changes in the turbine blade shapes can be more easily accommodated by simply exchanging the corresponding sub-domain. On the rotating turbine blade, a high speed flow occurs near the blade tip and low pressure appears near the leading edge and at the blade tip on the suction side. Accurate prediction of the low pressure on the suction side is necessary for high fidelity performance prediction of turbines. Thus, the blade surface near the leading edge, trailing edge, and blade tip were filled with finer

cells. An unstructured mesh consisting of 1.6 million cells in the domain were generated in the above-mentioned way and employed for the computations. In order to ensure that the hybrid mesh used in the present CFD procedure was acceptable for the baseline turbine design, the CFD solutions obtained on a fully structured hexahedral cell mesh were compared. Generally, it is known that a lower number of cells are required for the same level of accuracy if a structured hexahedral cell mesh is used. Therefore, a total cell count of about 0.59 million was used for the structured mesh. On each blade surface, 40 and 120 cells were put in the chordwise and spanwise directions. As for the hybrid mesh, finer cells were used near the blade tip, the leading and trailing edges. The turbine performance and the flow around the blade were compared at the design TSR. For fair comparison, the same computational methods and conditions were used, except for the mesh. The power coefficient (C P ¼ P=0:5qAU 3 ) prediction was 0.4610 with the hybrid mesh and 0.4564 with the structured mesh. The

(a) Lift coefficient

(b) Drag coefficient Fig. 6. Power coefficient for the turbine.

Fig. 7. Hydrofoil characteristics of NACA63-418.

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performance of a turbine but also for that of the cavitation performance. As shown in Fig. 5, the pressure coefficient contours and streamlines are in good agreement with each other. Based on these results, it is confirmed that hybrid meshing is quite acceptable for the prediction of the turbine performance. To verify the developed CFD procedure, the data from the model-scale experiment reported by Bahaj et al. [11] were used. Bahaj et al. [11] carried out a series of experiments with a three-bladed 800 mm diameter turbine in a 2.4 m  1.2 m cavitation tunnel and a 60 m long towing tank for the cavitation and power performance. The blade geometry was defined with 17 sections in the spanwise direction. Each blade section took the profile shape of the NACA 63-8xx. The experimental results for the power coefficients were presented for a wide range of TSRs. The turbine performance was analyzed for a yaw angle of 0° and for a set angle of 10°. The turbine dimensions and the inflow velocity of 1.3 m/s were the same for both the measurements and the CFD computations. Note that the hub, however, was not considered in the CFD prediction. Fig. 6 compares the power coefficient over a range of TSRs predicted by various methods including other numerical methods [7,13]. The present CFD results agree well with the experimental data and actually better in most cases than that of the other numerical simulations.

Fig. 8. Power coefficient predicted by BEMT.

Table 3 Numerical uncertainty assessment.

CP

e GCI

4. Results and discussion

Coarse

Medium

Fine

p/RE

0.361

0.460 0.2154 0.0027

0.461 0.0027 0.0000

13.02/10.03

4.1. BEMT results

two predictions were in excellent agreement with each other having a difference of only 1%. The comparison of the surface pressure coefficient (C press ¼ ðP L  PO Þ=0:5qU 2 ) contours on the suction side is shown in Fig. 4. Both the lowest pressure value and the overall pressure contours were predicted quite closely. The pressure coefficient contours and streamlines on the cross sections at r/R = 0.8 and 0.9 are shown in Fig. 5. Due to the high revolution speed near the blade tip, the lowest pressure occurs around these sections. Therefore, accurate reproduction of the flow field at these sections is quite important not only for the analysis of the power

The turbine power performance was analyzed for a set angle of 0°. The 2D hydrofoil characteristics of the NACA63-418 were obtained over a wide range of angles of attack using CFD simulations. The 2D simulations were performed with a constant Reynolds number of 3.0  106. Actually, the Reynolds number varied at different spanwise locations, but the difference in the hydrodynamic characteristics due to the change in the Reynolds number was assumed to be small enough. Fig. 7 shows the lift and drag coefficients obtained from the 2D CFD simulations along with that from Abbott and von Doenhoff [14]. There was good agreement between the two, suggesting that the 2D hydrofoil characteristics obtained using the CFD are reliable. For the performance prediction using BEMT, 14 blade sections at r/R = 0.3–1.0 were considered. The hub fitting part under r/

(a) Suction side

(b) Pressure side Fig. 9. Pressure coefficient contours of the pressures and suction sides.

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(a) r/R = 0.25

(b) r/R = 0.5

(c) r/R = 0.75

(d) r/R = 0.85

Fig. 10. Pressure coefficient contours and streamlines of the cross-sections.

R = 0.3 was not considered since its contribution to the turbine performance was insignificant. Fig. 8 shows the predicted values for the performance of the baseline turbine, presenting a typical trend of the power performance curve for a three-bladed tidal turbine. Note that the peak power coefficient, which was 0.459, was predicted at the design TSR. 4.2. CFD results The uncertainty in the computational simulations was assessed for the power coefficient with three different meshes. The coarse (0.77 million cells), medium (1.38 million cells), and fine (2.48 million cells) meshes in the sub-domain near the turbine blade

were considered. The estimated order of accuracy was calculated as

p¼

ln½ðumedium  ucoarse Þ=ðufine  umedium Þ lnðrÞ

ð10Þ

where ucoarse, umedium, and ufine are solutions at the coarse, medium, and fine levels, respectively; r is the effective mesh  1=D  1=D N ¼ NNmedium ¼ 1:8, with the cell refinement ratio of N fine coarse medium

count, N, and the number of dimensions, D. The Richardson extrapolated value (RE) and the convergence index (CI) were also calculated by Equations (11) and (12), respectively, as

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(a) Baseline turbine

Fig. 11. Power coefficients predicted by BEMT and CFD.

Fig. 12. Raked tip blade.

(b) Rounded tip turbine

Fig. 13. Power coefficients between the baseline turbine and the raked tip turbine.

RE ¼ ufine þ

ðufine  umedium Þ rp  1

ð11Þ

(c) Raked tip turbine Fig. 14. Contours of r + Cpress at an 8 m tip immersion for the raked tip turbine.

CI ¼ jej=ðr p  1Þ

ð12Þ

where

  u  u   fine medium  jej ¼     ufine

ð13Þ

Table 3 summarizes the numerical uncertainty assessment results. Overall, the solutions show good mesh convergence behavior with errors from the corresponding RE of less than 0.3%.

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(a) Baseline turbine

(b) Rounded tip turbine

(c) Raked tip turbine Fig. 15. Vorticity magnitude contours and streamlines at the trailing edge cross section.

With the verified CFD procedure, the baseline turbine was analyzed. Fig. 9 shows the surface pressure coefficient contours on the suction and pressure sides at the design TSR. The lowest pressure was seen at the leading edge on the suction side near the blade tip. Meanwhile, the highest pressure was observed at the leading edge on the pressure side. The pressure difference between the two sides generates the lift force on the blade and thereby, the

torque on the turbine. From the pressure coefficient contours, it was obvious that most of the power was produced near the blade tip, where the revolution speed was high. The pressure coefficient contours and streamlines for several spanwise sections are shown in Fig. 10. The typical pattern for the surface pressure distribution, including the low pressure region on the suction side near the blade tip, was well reproduced. The

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flow field displayed a well-behaved, attached flow at the design TSR, which is appropriate to extract the maximum lift force near the blade tip. However, near the hub, due to its elliptical shape and large angle of attack, the streamlines displayed nearseparation that may result in a slight drag increase. Fig. 11 shows the predicted power coefficient curve of the baseline turbine obtained by BEMT and CFD. Overall, the results were similar to each other and exhibited the essential features such as the general trend of the power coefficient curve and the peak value at the design TSR. The difference, however, was non-trivial at TSR < 4 and TSR > 8. The reason for the difference at the low TSRs can be explained by a phenomenon called stall delay. In BEMT, it was assumed that there was zero spanwise flow, i.e., no 3D flow. However, in reality, cross-flow in the spanwise direction exists due to the centrifugal force on the rotating turbine, and the unstable cross-flow results in stationary and traveling cross-flow vortices. The cross-flow instabilities cause separation delays, lift increase, and drag reduction [15]. Due to this stall delay, in other words, inaccurate hydrofoil characteristics at high angles of attack, the power output of turbines analyzed by BEMT is normally underestimated at low TSRs than its corresponding field performance [16]. On the other hand, the difference at high TSRs can be attributed to the turbulent windmill state, which takes place due to large axial induction factors. However, this rarely happens during normal operations; thus, consideration of the turbulent windmill state was only needed for the completeness of the method. In any event, it was confirmed that BEMT offered a rough estimation of turbine performance and CFD provided a detailed flow feature around the turbines and more accurate performance estimations. 4.3. Suggestion of new blade designs for cavitation inception delay Since HATSTs are operated in water, measures to avoid cavitation, which has negative impact on the performance of hydrodynamic mechanical devices, e.g., noise and vibration, are needed. To reduce the hydrostatic pressure at the blade tip and at the tip vortex [17], the blade tip of the baseline turbine was modified. Firstly, the blade tip was rounded from r/R = 0.95, and dubbed the rounded tip turbine. Secondly, the blade tip was rounded and bent from r/R = 0.95 towards the suction side with a cant angle of 90°. Thus, it was termed the raked tip turbine. Fig. 12 shows the shape of a raked tip turbine blade. Fig. 13 shows the comparison of the power coefficients for the baseline and modified tip turbines over a range of TSRs. The power coefficient of the rounded tip turbine decreased by 3% compared to that of the baseline turbine. On the other hand, there was slight performance improvement with the raked tip turbine, especially at low TSRs. The reason for this improvement at low TSRs was due to the mitigated tip vortex at high incidence angles. The contours of r + Cpress on the baseline, rounded, and raked tip turbines are shown for an 8 m tip immersion in Fig. 14. Cavitation inception was defined as the state when the value of r + Cpress drops below zero. For the baseline turbine, cavitation inception was observed when the tip immersion was below 8 m. The lowest value was observed at the trailing and leading edges of the tip section. On the other hand, at the same tip immersion, cavitation inception was not yet observed in the rounded and raked tip turbines. For the rounded and raked tip turbines, the value of r + Cpress dropped below zero at 6.8 m and 6.6 m tip immersions, respectively. In other words, the cavitation inception was delayed due to the design change in the shape of the blade tip. To ensure that the tip vortex was reduced in the rounded and raked tip turbines, the vorticity magnitude at the blade tip was compared. Fig. 15 shows the vorticity contours at a cross section near the trailing edge. The vorticity contours and streamlines at the blade tip and pressure contours on the turbine blade are also

shown. As expected, the vortex from the pressure side to the suction side was significantly suppressed in the rounded and raked tip turbine. However, the raked tip turbine should be appraised better because there was no loss of the turbine performance as for the rounded tip turbine. 5. Concluding remarks Two computational procedures based on BEMT and CFD were developed for efficient and convenient performance prediction of HATST, and based on the procedures, a new blade design was proposed for cavitation inception delay. (1) For the BEMT procedure, an in-house BEMT code was developed. 2D hydrofoil characteristics obtained by CFD were used for the performance analysis of the baseline turbine. The results for the performance prediction of the baseline turbine using BEMT was similar to that using CFD around the design TSR. This confirms that the BEMT procedure is quite the useful tool for turbine performance prediction near the design TSR. (2) The CFD method was used for the 3D full-scale HATST performance analysis. The rotating reference frame along with a hybrid meshing approach was proposed for a convenient and easy turbine performance analysis. With the hybrid meshing approach, design changes in the turbines can be easily considered by switching the sub-domain for the blade. The results using the present CFD procedure were compared to the results obtained with a fully structured mesh and the results were quite similar to each other. The procedure using CFD is useful for more detailed flow features around a turbine and for a more accurate performance estimation. (3) A new turbine design, which has a raked tip shape for cavitation inception delay and noise reduction, was presented. The cavitation performance of the raked tip turbine was analyzed using the present CFD procedure. The results showed that the cavitation performance of the raked tip turbine improved with the slight tip shape change without degrading the turbine performance.

Acknowledgments This work was supported by the Ministry of Knowledge Economy (20093021070010 and 20104010100490), and the Ministry of Education, Science and Technology (R32-2008-000-10161-0). References [1] MacLeod AJ, Barnes S, Rados KG, Bryden IG. Wake effects in tidal current turbine farms. In: Proceedings of marine renewable energy conference. Newcastle (UK); 2002. [2] Khan MJ, Bhuyan G, Iqbal MT, Quaicoe JE. Hydrokinetic energy conversion systems and assessment of horizontal and vertical axis turbines for river and tidal applications: a technology status review. Appl Energy 2009;86:1823–35. [3] Coiro DP, Maisto U, Scherillo F, Melone S, Grasso F. Horizontal axis tidal current turbine: numerical and experimental investigations. In: Proceedings of offshore wind and other marine renewable energies in Mediterranean and European seas. Civitavecchia (Italy); 2006. [4] Clarke JA, Connor G, Grant AD, Johnstone C. Design and testing of a contrarotating tidal current turbine. Proc Inst Mech Eng Part A: J Power Energy 2007;221(2):171–9. [5] Batten WMJ, Bahaj AS, Molland AF, Chaplin JR. The prediction of the hydrodynamic performance of marine current turbines. Renew Energy 2008;33:1085–96. [6] Mason-Jones A, O’Doherty T, O’Doherty DM, Evans PS, Wooldridge CF. Characterisation of a HATT using CFD and ADCP site data. In: Proceedings of 10th world renewable energy congress, Grasgow, UK, 2008. [7] Kinnas SA, Xu W. Analysis of tidal turbines with various numerical methods. In: Proceedings of 1st annual MREC technical conference, MA, USA, 2009.

J.H. Lee et al. / Applied Energy 98 (2012) 512–523 [8] Harrison ME, Batten WMJ, Myers LE, Bahaj AS. A comparison between CFD simulations and experiments for predicting the far wake of horizontal axis tidal turbines. In: Proceedings of 8th European wave and tidal energy conference. Uppsala (Sweden); 2009. [9] Lee SH, Lee SH, Jang K, Lee J, Hur N. A numerical study for the optimal arrangement of ocean current turbine generators in the ocean current power parks. Curr Appl Phys 2010;10:137–41. [10] McCombes T, Johnstone C, Grant A. Unsteady 3D wake modeling for marine current turbines. In: Proceedings of 8th European wave and tidal energy conference. Uppsala (Sweden); 2009. [11] Bahaj AS, Molland AF, Chaplin JR, Batten WMJ. Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renew Energy 2007;32:407–26. [12] Weiss JM, Smith WA. Preconditioning applied to variable and constant density flows. AIAA J 1995;33(11):2050–7.

523

[13] Baltazar J, Falcao de Campos JAC. Unsteady analysis of a horizontal axis marine current turbine in yawed inflow conditions with a panel method. In: Proceedings of 1st international symposium on marine propulsors. Trondheim (Norway); 2009. [14] Abbott IH, von Doenhoff AE. Theory of wing section: including a summary of airfoil data. 1st ed. New York: Dover Publication; 1959. [15] Gross A, Fasel HF, Friederich T, Kloke MJR. Numerical investigation of S822 wind turbine airfoil. In: Proceedings of 40th fluid dynamics conference and exhibit. Chicag (USA); 2010. [16] Tangler L. Comparison of wind turbine performance prediction and measurement. J Sol Energy Eng 1987;104(2):84–8. [17] Johansen J, Sorensen NN. Numerical analysis of winglets on wind turbine blades using CFD. In: Proceedings of European wind energy conference & exhibition. Milan (Italy); 2007.